Infrared single-photon detection with superconducting magic-angle twisted bilayer graphene

The moiré superconductor magic-angle twisted bilayer graphene (MATBG) shows exceptional properties, with an electron (hole) ensemble of only ~1011 carriers per square centimeter, which is five orders of magnitude lower than traditional superconductors (SCs). This results in an ultralow electronic heat capacity and a large kinetic inductance of this truly two-dimensional SC, providing record-breaking parameters for quantum sensing applications, specifically thermal sensing and single-photon detection. To fully exploit these unique superconducting properties for quantum sensing, here, we demonstrate a proof-of-principle experiment to detect single near-infrared photons by voltage biasing an MATBG device near its superconducting phase transition. We observe complete destruction of the SC state upon absorption of a single infrared photon even in a 16–square micrometer device, showcasing exceptional sensitivity. Our work offers insights into the MATBG-photon interaction and demonstrates pathways to use moiré superconductors as an exciting platform for revolutionary quantum devices and sensors.


Hysteretic I-V curves in superconducting MATBG devices
For this project we have produced several MATBG superconducting devices with the 'cut-andstack' procedure described in the methods section.Among all the superconducting MATBG we have selected 3 devices which featured sharp superconducting transitions with hysteretic I-V characteristics and investigated their photoresponse.
Device A and C have a single bottom graphite back gate, while device B has an additional graphite top-gate which was picked up at the first step of the stacking process.The global twist angles measured from transport data for device A, B and C are  = 1.04°,  = 1.03° and  = 1.16° respectively.
As detailed in the main text, we attribute the presence of a hysteretic loop in the I-V curves to a current-induced self-heating hotspot when the MATBG is in the normal state.In Fig. S4 we show the I-V curves of devices A, B and C at different temperatures and gate voltages (corresponding to different carrier densities).In all devices the hysteresis loop disappears for temperatures T ~ 1 K.We also point out that the applied gate voltage provides high tunability on the critical current and on the width of the hysteretic loop.This represents an important tuning knob to engineer and design the electronic circuit.In order to control the hysteretic loop in the MATBG device, we implement the voltage-biased scheme detailed in Fig. 1c of the main text.In the voltage-biased scheme, the increase of resistance induced when the MATBG detector is in the normal state, reduces the current flowing in it and brings the device back to the superconducting state.In Fig. S5 we observe the I-V curves for device A, B and C measured in the current-biased scheme (top) and in the voltagebiased scheme (bottom).We notice that in all devices the hysteresis loop present in the currentbiased scheme is completely closed in the voltage-biased one.The simple reset circuitry described here, prevents permanent 'latching' of the detector in the normal state and allows us to reset it after photo-absorption.

Optoelectronic setup
As explained in the Methods section an illustrated in Fig. S6, to perform the photoresponse measurements we placed the device in a dilution refrigerator and provided optical excitation with a 1550-nm laser diode coupled through a telecom single-mode optical fiber.

Beam profile at the sample stage
As shown in Fig. S7, in our setup we couple a telecom laser which emits an output power Pout with a single-mode optical fiber designed for 1550-nm transmission.The fiber is then connected to a laser beam coupler which provides a collimated output with beam radius w0 ∽ 2 mm and Rayleigh range zR =  0 2  ~ 8 m.In order to quantitatively describe the light-induced count rate on the MATBG detector we consider a Gaussian beam profile.In this approximation, the intensity profile I as a function of the distance from the beam center r and distance away from the end of the coupler  reads (38): Where w(z) is the value of the radius at a distancez from the fiber given (38) by () =  0 √1 + (/  ) 2 and  0 = 2  /( 0 2 ) is the total irradiance coming out of the laser source imposing the Gaussian normalization condition.In Fig. S7c we simulate w(z) up to 1 m of distance from the fiber coupler.Since in our experimental configuration the device is around z0 ~ 3 cm away from the fiber coupler (  0   = 0.0037 << 1) we can consider the beam to be collimated and replace in (Eq.1) () ≃  0 = 2 mm.Since we align the device to be roughly at the center of the beam (Eq.1) reads ( = 0,  0 ) =

Calculation of the power density incident on the MATBG device
With the considerations made in the previous section, we can calculate the power density PL incident on the MATBG: Where Pout is the total power output coming out of the laser, Tfiber = 0.021 the effective transmission of the fiber and all the optical connections and η the variable attenuation (in dB) we use to control the power incident on the device.In the single-photon measurements with the CW laser source we keep the laser power constant (Pout = 11 µW for device A) and scan η between several order of magnitudes from 70 dB to 4 dB.For device A, a typical attenuation of 40 dB results in PL = 3.7 Given   , the average incident photon rate per unit time τ per µm 2 〈 ℎ 〉 reads: Where hν = 1.28 • 10 -19 J is the energy of a single photon at λ = 1550 nm.For an attenuation of 40 dB and τ = 5 ms, we expect 〈 ℎ 〉 = 0.14.
In pulsed experiments, by changing the laser repetition rate (fRR) we can control the number of photons carried on average by each pulse µ as: Where l1 ~ 3 µm and l2 ~ 5.3 µm are the length and width of the area between the two voltage probes (white dashed box in the optical image of Fig. 1f).Since we assume the sample to be located at the center of the beam and l1, l2 << w0 we can simplify (Eq.4) to: For a typical Pout = 3 nW, fRR = 100 Hz, and attenuation of 13 dB, we obtain µ = 0.62.
It is worth noticing that the calculated values are only an upper-bound estimation because the optical alignment is not controlled accurately in the cryogenic experiment.In particular it is possible that the sample is not perfectly located in the center of the beam and that the effective incident power is lower.

Estimation of the optical absorption in the heterostructure
To investigate the effect on the substrate in the internal efficiency we employ the transfer matrix method(53) assuming the radiation to be linearly polarized at 1550 nm and at normal incidence.Considering the refractive indexes and the thicknesses of the layers which constitute the heterostructure (hBN = 7 nm, MATBG= 0.69 nm, hBN = 5 nm, Graphite = 2 nm, SiO2 = 285 nm) we calculate an absorption of 5.3% for the MATBG layer, which is only slightly enhanced compared to the one expected for suspended MATBG at these excitation energies (4.6%).In our experiment the substrate was not properly engineered to enhance the MATBG absorption, but we envision that this could be achieved by implementing cavities (54) or photonic crystals (55), analogously to what was previously done in graphene.

Effective bandwidth of the electrical readout
In this section we measure the overall bandwidth of the electronic readout available in our experiment which determines the distortion of the electrical pulses and limits the reset circuitry.Assuming that our electronic readout effectively behaves as an ideal RC low-pass circuit, we characterize its performance by determining the minimum rise time of electrical pulses and evaluating the available 3-dB bandwidth.To obtain these parameters under conditions closely resembling our single-photon detection experiment, we place a resistor (10 kilohm) into the sample space and monitor the voltage across the resistor using a 4-terminal configuration (Fig. S9b).To measure the minimum rise time, defined as the length of time required for a signal to transition from the 10% to the 90% of the rising edge of the curve, we employ an arbitrary wavefunction generator (AWG) to generate square wave pulses with a frequency of 13.3 Hz.We record the voltage across the 10 kilohm resistor with an oscilloscope (Fig. S9a, b).By analyzing the square wave pulse (Fig. S9c) we extract the minimum rise time tr = 422 µs.From this measurement, we calculate the effective 3-dB cut-off frequency as: f3dB = 0.35/tr = 830 Hz.Additionally, we directly measure the 3-dB bandwidth by applying a sinusoidal ac current to the resistor at various frequencies ranging from 3 Hz to 100 kHz using a lock-in amplifier.We measure the voltage generated across the 10 kilohm resistor with a lock-in amplifier in the same configuration (see Fig. S9d).From this measurement we can extract the 3-dB bandwidth defined as the frequency at which the initial amplitude drops by 3-dB or 0.707 of its initial value.
We obtain f3dB = 738 Hz.The two different measurements give compatible results.
In Fig. S10a we report an example of the photovoltage generation, Vph, measured with an oscilloscope when the MATBG device is exposed to laser beam radiation of wavelength λ = 1550 nm.The measurement is performed in the configuration described in Fig. S6 using a roomtemperature low-pass filter with 10 kHz cut-off.Upon photon absorption, the MATBG detector transitions to the normal state, resulting in a maximum voltage output of Vph(Vbias) ≈ V(Vbias).Subsequently, the detector remains in the normal state for few ms (~ 1 ms for the trace in Fig. S10a) before the voltage bias circuit resets it to the superconducting state.It is worth noting that our observed pulse shape differs from the typical behavior observed in conventional superconducting single-photon detectors(3).In those detectors, the generated photovoltage exhibits a rapid spike followed by a slower decay with a characteristic time, τ (5,34,51,52).
We observe that the measured pulse rise time (tr = 356 µs) in our pulse shape (Fig. S10b) is extrinsically limited by the restricted bandwidth and compatible with the one measured with the 10 kilohm resistor.Similarly, the measured decay time is td ~ tr.Despite the restricted bandwidth available in our experiment, we are still able to properly study the statistics of the photoinduced counts and demonstrate single-photon sensitivity by the MATBG detector.
To improve the speed of readout, a possible path forward is to design a resonator-based readout, in which the kinetic inductance is part of the resonator.When an absorbed photon generates quasiparticles inside MATBG, its kinetic inductance increases and hence suppresses the resonance frequency.This concept is similar to the kinetic inductance detector (10) which has proven to provide a fast readout of SPD.

Method of registering counts in the detector
In this section we show how we derive the plots shown in Fig. 3 from the raw data and detail the methods used to extract the counts of the MATBG detector.As described in the Methods section, we acquire photovoltage time traces with an analog-to-digital converter or an oscilloscope.From the raw traces (as the ones shown in Fig. 2a of the main text) we use a MATLAB script to count the number of detected events by setting a threshold (Vph > 0.4 mV for device A) and a minimum distance between the clicks of 17 ms.We choose a minimum distance of 17 ms because the recovery time of the clicks varies as a function of the bias point from ~ 1 ms to ~ 17 ms.This limits the maximum measurable count rate to ~ 50 Hz.For the PCR vs PL measurements, the minimum distance between the clicks is 13 ms.
In Fig. S11a, we present the photon count rate (PCR) as a function of Vbias, measured at various laser powers (from no power up to 183 we also report the raw photovoltage time traces with and without illumination for six different bias points (vertical colored lines) from which we extracted the PCR vs. Vbias.In Fig. S12, we show the PCR vs. PL for Vbias = 0.995 Vc as in Fig. 3b of the main text and the raw photovoltage time traces for six different laser powers.

Linearity of photon counts for a highly attenuated coherent source
The light emitted by a laser source can be expressed as a coherent superposition of m-photon states, |⟩ (13,36): Here | 2 | is the average photon number in the coherent state, which is directly proportional to the average photon number absorbed in the detector within a certain time duration τ, i.e. | 2 |〈 Nphoton〉.The probability of detecting a m-photon state in a time window τ is then given by: For a highly attenuated laser source, i.e. | 2 | << 1, the higher probability is to have either no photons or single-photons, while the probability of multi-photons is smaller: (| = 0) ≫ (| = 1) ≫ (| ≥ 2).As the probability of single-photon events (m = 1) scales linearly with | 2 |, by analyzing the linear scaling of the photon count rate with 〈Nphoton〉 in Fig. 3B, we conclude that the MATBG detector is capable of detecting single-photons.

Single-photon sensitivity with pulsed light excitation
An independent way to cross-check the single-photon sensitivity observed under CW illumination is provided by measurements with pulsed light excitation.For this purpose, we use a ~ 50 ps laser source at λ = 1550 nm with broadly tunable repetition rate, fRR.The pulsed laser source allows independent control of both the number of photons carried on average by each pulse (µ) and of the frequency at which the pulses impinge on the device (inset of Fig. S13a).Having at disposal these tuning knobs, we demonstrate that the MATBG detector responds to pulses with less than one photon on average and confirm the linearity of singlephoton sensitivity even under pulsed light excitation.
First, we measure the count rate at different fRR spanning over several orders of magnitude from 10 Hz to 1 MHz while fixing the number of photons carried on average by each pulse, µ.Specifically, we keep µ = PLA/hνfRR = 0.62 < 1 fixed by tuning simultaneously fRR and PL.Here A ~ 16 µm 2 is the area between the two voltage probes.Arguably, the effective area contributing to the photoresponse is smaller than A because of the twist angle inhomogeneity and the absorption is expected to be only a few percent, implying that the µ calculated here serves as an upper limit.Having fixed µ < 1, the majority of pulses incident in the area A carry either 0 or 1 photon and the probability of a pulse carrying 2 photons is negligible.Fig. S13a illustrates the extracted detection efficiency (defined as the ratio of counts detected per second to photons incident per second in the area A) plotted against the laser repetition rate, revealing three distinct regimes.For fRR < 100 Hz the detection efficiency decreases until it reaches a plateau which persists up to fRR ~ 30 kHz.After this plateau, the detection efficiency abruptly drops.In the low repetition rate regime, the count rate is dominated by the dark counts: the rate at which the pulses carrying 1 photon are absorbed is lower than the dark count rate, resulting in a detection efficiency higher than the effective one.Within the range of repetition rates where we observe a plateau, the detection efficiency remains unaffected by the time distance between the pulses, indicating that the absorbed photon rate is smaller than the detector recovery time.This rules out steady state heating from the laser source for average powers below < 300 aW/µm 2 .From the inset in Fig. S13a we observe that in this range of powers the PCR scales linearly with the average number of photons absorbed per second, confirming that the MATBG is operating as a single-photon detector.The drop of detection efficiency observed at high repetition rates is instead attributed to a saturation of the MATBG detector count rate and consistently occurs at the same average powers as in the CW experiment (> 300 aW/µm 2 ).Subsequently, we fix the repetition rate to 5 kHz, where the detection efficiency is independent of fRR, and change the average laser power to control the number of photons carried on average by each pulse.Fig. S13b demonstrates that when the mean photon number per pulse is less than 1, the count rate evolves linearly with μ for two distinct bias voltages over several orders of magnitude.This observation further validates the single-photon sensitivity under pulsed excitation.

Additional photoresponse data of device A
For completeness we report additional photoresponse data measured on device A. In Fig. S14a we plot the PCR vs. Vbias measured at various laser powers as in Fig. 3a of the main text but in linear scale.In the linear scale it is possible to see the sigmoidal shape with tendency to saturation.Specifically, in Fig. S14b, we plot the PCR vs. PL in correspondence of these saturation plateaus and show that they evolve linearly with laser power ruling out an artifact form the limited bandwidth.In Fig. S14c we plot the PCR vs. PL measured at a different bias point (Vbias = 0.991 Vc) than the ones reported in Fig. 3 of the main text.Even at this Vbias the MATBG detector shows single-photon sensitivity.
We also measure the PCR vs. PL measured at T = 700 mK and Vbias = 0.996 Vc (Fig. S15) and observe a linear scaling of the PCR with PL, demonstrating single-photon sensitivity up to this temperature.

Photovoltage generation and pulse shape
Here we show the pulse shapes measured for the three devices and discuss the origin of the photovoltage generated in MATBG devices.We argue that the photovoltage studied here is due to a complete breaking of the superconducting state upon absorption of a photon.In Fig. S16 we show the oscilloscope traces recorded while sweeping the bias voltage across the transition in both directions from the superconducting to normal state and vice-versa.By comparing them with the pulse shapes measured for device A, B and C (at Vbias = 0.989 Vc, Vbias = 0.991 Vc and Vbias = 0.9994 Vc respectively) we notice that the voltage output induced by the photons matches the voltage generated by manually sweeping the device across the transition.

Photoresponse of device B
In this section we summarize the optoelectronic measurements performed on device B. As discussed in the transport characterization, device B features I-V curves very similar to device A but the superconducting state is not fully developed since it does not reach zero resistance (Fig. S4e).We attribute this to twist angle inhomogeneity (44).In this device we measure the photovoltage time traces using the exact same setup and circuit presented above and also observe voltage spikes which increase as we increase the incident laser power.However, we observe a substantial increase of the dark count rate in device B, compared to device A. For instance, at Vbias ~ 0.99 Vc, device A exhibits a dark count rate of approximately 10 -3 Hz, while device B of around 3 × 10 -1 Hz (see Fig. S18).In SPDs, the superconducting gap typically protects the superconducting state from external excitations that turns the superconductor normal and results in dark counts.We can expect a higher dark count in device B because of the non-zero resistive state observed in the transport characterization.

Photoresponse of device C
In this section we summarize the optoelectronic measurements performed on device C. Device C features different I-V characteristics than device A and B because it has a smaller hysteresis loop (~ 2-3 nA).In addition, while device A and B feature a sharp transition from superconducting to normal state, device C shows a smooth transition.In Fig. S19 we show the lightinduced switching events recorded in device C and in Fig. S19 we summarize the analysis performed on these photovoltage time traces.

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Fig. S1.| Full characterization of the superconducting state of device A at ν = -2.45.(a).Currentvoltage (I-V) curves measured at different temperatures and plotted in logarithmic scale.The logarithmic scale helps in determining the Berezinskii-Kosterlitz-Thouless transition temperature (TBKT ~ 1.6 K) by fitting the data to a power law V ∝ I 3 (represented by the blue dashed line).(b) Differential resistance dVxx/dI as a function of bias current Ibias and out-of-plane magnetic field B for ν=-2.45.The ac excitation current used for this measurement is Iac = 2 nA.The superconducting state is completely smeared out by magnetic field at B ~ 150 mT.

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Fig. S2.| Transport characterization with out-of-plane magnetic field for device A. (a) Landau fan diagram measured at 35 mK with an excitation current of 10 nA and an applied out-of-plane magnetic field B ranging from 0 to 4 T. (b) Low-field Hall density measurements.The light-gray line trace shows the Hall carrier density nH versus the moiré band filling factor ν measured at 500 mT.The light green stripes indicate the position of correlated states while the light red ones the band insulating states.The thick red lines delineate the regions where the Hall carrier density exhibits a linear relationship with the filling factor.Notably, at the integer fillings corresponding to the correlated states, we observe resets of the Hall carrier density, resulting in the presence of extremely low carriers involved in the conduction process.Specifically, for the doping used in the single-photon detection experiments (ν between -2 and -3) we expect a carrier density nH ~ 10 11 cm -2 .

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Fig. S3.| Optical images of the measured devices.The scale bar in all the images is 3 µm.Device A and C have a single bottom graphite back-gate while device B has a double graphite gate.

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Fig. S4.| Current-biased I-V curves at different temperatures and gate voltages.(a)-(c) Currentbiased I-V curves at 3 different temperatures for device A, B and C respectively.The I-V curves are measured at the doping (gate voltages) used for photodetection which are -0.620V, -0.566V and -0.8257 V for device A, B and C respectively.In all the 3 devices the hysteresis loop disappears for temperatures ~ 1 K. (d)-(f) Current-biased I-V curves at different gate voltages (carrier densities) and T = 35 mK within the superconducting dome for device A, B and C respectively.

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Fig. S5.| Current-biased and voltage-biased I-V curves.(a)-(c) Current-biased I-V curves for device A, B and C. The bias current is provided by a voltage source in series with a 10 Megaohm resistor.The I-V curves are measured at the doping used for photodetection which are -0.620V, -0.566V and -0.8257 V for device A, B and C respectively.(d)-(f) Voltage-biased I-V curves for device A, B and C measured at the same doping.The bias voltage is provided by a voltage source in series with a 1/1000 voltage divider.As described in the main text the load resistor is much smaller than the residual resistance arising from the contact resistance and the metallic leads (R2 << Rres.).R1 = 1 Megaohm, R2 = 1 kilohm for device A and B while R1 = 100 kilohm, R2 = 100 ohm for device C.

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Fig. S6.| Optoelectronic setup.Schematics of the optoelectronic setup employed to measure the photoresponse in the MATBG superconducting detector.

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Fig. S7.| Beam profile at the sample stage.(a) Optical image of the experimental scheme.The singlemode optical fiber designed 1550-nm transmission is connected to a laser beam coupler which provides a collimated output.The sample is located at around 3 cm far from the fiber coupler.(b) 3D plot of the normalized beam intensity in the Gaussian beam approximation.(c) Simulation of the Gaussian beam radius w(z) at a distance z from the fiber coupler () =  0 √1 + (/  ) 2 .The black vertical line is the position of the sample zs = 3 cm.

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Fig. S8.| AFM and optical micrographs for device A. (a) The main panel is the optical image of the final hBN/MATBG/hBN/Graphite stack.The inset shows an AFM scan of the final device etched into a Hall bar geometry.The dashed square indicates the area imaged with the AFM.The lower panel shows the height profiles taken along the blue and red dashed lines from which we extract the hBNs and graphite thicknesses.(b) Schematic cross-section of the stack used in the transfer matrix calculations.The second layer of the heterostructure is the active one.

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Fig. S9.| Minimum rise time and frequency response magnitude of the electrical readout.(a) Voltage signal measured with an oscilloscope across a 10 kilohm resistor when excited with a square wave of frequency 13.3 Hz.(b) Schematics of the circuit used to measure the rise time and the 3-dB bandwidth.(c) Zoom of the voltage traces from which we extract the rise time of the square wave pulse.(d) Measured frequency response magnitude of the readout.

aW μm 2
Fig. S10.|Pulse shape, rise time and decay time for device A. (a) Photovoltage pulse Vph measured in the MATBG photodetector at Vbias/Vc ~ 0.989 and λ = 1550 nm with a single-shot oscilloscope.(b) Rise time tr = 356 µs measured from the pulse in (a) which results in an overall bandwidth of the electronic readout of < 1 kHz.(c) The decay time td is similar to the rise time.

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Fig. S11.|Raw photovoltage time traces for different bias points.(a) Photon count rate (PCR) vs. Vbias measured for different laser powers as in Fig. 3a.(b)-(g) Raw photovoltage time traces with and without 1550 nm laser-illumination for different bias points.

Fig. S12 .
Fig. S12.|Raw photovoltage time traces for different laser powers.(a) Extracted photon count rate (PCR) versus laser power for Vbias = 0.995 Vc as shown in Fig. 3b of the main text.The colored dots are the selected laser powers for which we show the raw photovoltage time traces.(b)-(g) Raw photovoltage time traces measured over time for laser powers ranging over 5 orders of magnitude (laser attenuation from 70 dB to 22 dB).The black dashed line represents the threshold for counting the clicks.If the generated photovoltage is Vph > 0.4 mV, we register a count in the detector.(b)-(d) Raw photovoltage time traces measured over 2000 second for attenuations of 70, 62 and 52 dB.In this range, the PCR (< 0.02 Hz) is not affected by the increase of laser power, meaning that the observed counts are mostly due to false positive (dark) counts.(e)-(g).Raw photovoltage time traces measured over 200, 20 and 2 seconds for attenuations of 42, 32 and 22 dB respectively.In these plots we scale the time duration of the traces inversely with the laser attenuation to facilitate the counting of the 'clicks' and allow to derive the PCR by eye.In this range, we observe that the PCR scales linearly with the incident power: 42 dB (PCR ~ 0.15 Hz), 32 dB (PCR ~ 1.5 Hz) 22 dB (PCR ~ 14 Hz).

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Fig. S13.|Single-photon sensitivity with pulsed light excitation.(a) Detection efficiency measured at fixed mean photon number per pulse µ = 0.62 and different laser repetition rates, fRR for Vbias = 0.995 Vc.Here the detection efficiency is defined as counts detected per second over photons incident per second in the area marked by the two voltage probes (A ~ 16 µm 2 ).On the top x-axis the average incident power density PL corresponding to each fRR.The solid line highlights the plateau in detection efficiency observed between 100 Hz to 30 kHz.Inset: photon count rate, PCR versus the average incident photon number 〈Nphoton〉 in 1-s time window per µm 2 .The solid line is a linear fit with an offset due to dark counts.(b) PCR versus µ for two different bias points at a fixed fRR = 5 kHz.The solid lines are linear fits (with an offset due to dark counts), showing that the PCR evolves linearly with µ.

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Fig. S15.|Single-photon sensitivity at T = 700 mK.PCR vs. average incident photon number 〈Nphoton〉 at T = 700 mK and Vbias = 0.996 Vc.The solid line is a linear fit (with an offset due to dark counts) demonstrating single-photon sensitivity up to 700 mK.

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Fig. S14.|Additional photoresponse data of device A. (a) Extracted photon count rate (PCR) vs. Vbias measured at various laser powers and plotted in linear scale.(b) PCR vs. PL in correspondence of the saturation plateaus ~ 0.997 Vc.(c) PCR vs. PL measured at Vbias = 0.991 Vc.The MATBG detector shows single-photon sensitivity even at this bias point.

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Fig. S16.|Photovoltage generation and pulse shape for all devices.(a)-(c) Typical pulse shape measured with a single-shot oscilloscope upon photo-absorption for device A, B and C at Vbias = 0.989 Vc, Vbias = 0.991 Vc and Vbias = 0.9994 Vc respectively.(d)-(f) Single-shot oscilloscope traces recorded while sweeping the bias voltage across the transition in both directions from the superconducting to normal state (blue) and vice-versa (red).

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Fig. S17.|Raw photovoltage time traces at different laser powers for device B. (a)-(c) Raw photovoltage time traces measured over time for 3 laser powers.The black dashed line represents the threshold for counting the clicks.If the generated photovoltage is Vph > 0.5 mV, we register a count in the detector.

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Fig. S18.|Photoresponse of device B. (a) Photon count rate (PCR) vs. Vbias measured with and without 1550 nm laser-illumination.(b) Extracted photon count rate PCR versus laser power for the bias points indicated by the vertical dashed line in (b).The solid line is a linear fit.

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Fig. S19.|Raw photovoltage time traces at different laser powers for device C. (a-c) Raw photovoltage time traces measured over time for 3 laser powers.The black dashed line represents the threshold for counting the clicks.If the generated photovoltage is Vph > 0.325 mV, we register a count in the detector.

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Fig. S20.|Photoresponse of device C. (a) Photon count rate (PCR) vs. Vbias measured with and without 1550 nm laser-illumination.(b) Extracted photon count rate PCR versus laser power for the bias points indicated by the vertical dashed lines in (b).